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  • 1
    Electronic Resource
    Electronic Resource
    Grassmannian Fixed Point Ratios (2000)
    Springer
    Geometriae dedicata 82 (2000), S. 21-104 
    Details
    ISSN: 1572-9168
    Keywords: fixed point ratios ; almost simple groups ; permutation actions ; classical groups.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide estimates for the fixed point ratios in the permutation representations of a finite classical group over a field of order q on k-subspaces of its natural n-dimensional module. For sufficiently large n, each element must either have a negligible ratio or act linearly with a large eigenspace. We obtain an asymptotic estimate in the latter case, which in most cases is q −dk where d is the codimension of the large eigenspace. The results here are tailored for our forthcoming proof of a conjecture of Guralnick and Thompson on composition factors of monodromy groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005278605358
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  • 2
    Electronic Resource
    Electronic Resource
    Irreducibility of alternating and¶symmetric squares (1998)
    Springer
    Manuscripta mathematica 95 (1998), S. 169-180 
    Details
    ISSN: 1432-1785
    Keywords: Mathematics Subject Classification (1991): 20E28, 20G40, 20C20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract: We investigate the question when the alternating or symmetric square of an absolutely irreducible projective representation of a non-abelian simple group G is again irreducible. The knowledge of such representations is of importance in the description of the maximal subgroups of simple classical groups of Lie type. We obtain complete results for G an alternating group and for G a projective special linear group when the given representation is in non-defining characteristic. For the proof we exhibit a linear composition factor in the socle of the restriction to a large subgroup of the alternating or symmetric square of a given projective representation V. Assuming irreducibility this shows that the dimension of V has to be very small. A good knowledge of projective representations of small dimension allows to rule out these cases as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002290050021
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    Paper (German National Licenses)
    Fulltext
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